Quasi-Contractions on Kreĭn Spaces View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1993

AUTHORS

Aurelian Gheondea

ABSTRACT

A quasi-contraction, acting between Kreĭn spaces, is a linear bounded operator which is contractive when restricted to some subspace of finite codimension. If, in addition, the same property is satisfied by the adjoint of the operator, then it is called a double quasi-contraction. This paper is devoted to the investigation of basic properties of quasi-contractions and double quasi-contractions. Among others, we prove that the compression of a quasi-contraction (double quasi-contraction) to maximal uniformly negative subspaces is a semi-Fredholm operator (respectively, Fredholm operator) and we give a formula to compute its index. A spectral characterization of double quasi-contractions within the class of quasi-contractions is also obtained. More... »

PAGES

123-148

References to SciGraph publications

  • 1974. Indefinite Inner Product Spaces in NONE
  • 1990. Extension Theorems for Contraction Operators on Kreĭn Spaces in EXTENSION AND INTERPOLATION OF LINEAR OPERATORS AND MATRIX FUNCTIONS
  • 1982. Spectral functions of definitizable operators in Krein spaces in FUNCTIONAL ANALYSIS
  • Book

    TITLE

    Operator Extensions, Interpolation of Functions and Related Topics

    ISBN

    978-3-0348-9687-0
    978-3-0348-8575-1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-0348-8575-1_7

    DOI

    http://dx.doi.org/10.1007/978-3-0348-8575-1_7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1040296755


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "name": [
                "Institutul de Matematic\u0103, al Academiei Rom\u00e2ne, C.P. 1-764, 70700, Bucure\u015fti, Rom\u00e2nia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Gheondea", 
            "givenName": "Aurelian", 
            "id": "sg:person.016700571527.26", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016700571527.26"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bfb0069840", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006857348", 
              "https://doi.org/10.1007/bfb0069840"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-65567-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011407145", 
              "https://doi.org/10.1007/978-3-642-65567-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-65567-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011407145", 
              "https://doi.org/10.1007/978-3-642-65567-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-0348-7701-5_5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026233832", 
              "https://doi.org/10.1007/978-3-0348-7701-5_5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/mana.19770770116", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027367955"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-1236(92)90124-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043655855"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1307/mmj/1029003552", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064976412"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1993", 
        "datePublishedReg": "1993-01-01", 
        "description": "A quasi-contraction, acting between Kre\u012dn spaces, is a linear bounded operator which is contractive when restricted to some subspace of finite codimension. If, in addition, the same property is satisfied by the adjoint of the operator, then it is called a double quasi-contraction. This paper is devoted to the investigation of basic properties of quasi-contractions and double quasi-contractions. Among others, we prove that the compression of a quasi-contraction (double quasi-contraction) to maximal uniformly negative subspaces is a semi-Fredholm operator (respectively, Fredholm operator) and we give a formula to compute its index. A spectral characterization of double quasi-contractions within the class of quasi-contractions is also obtained.", 
        "editor": [
          {
            "familyName": "Gheondea", 
            "givenName": "A.", 
            "type": "Person"
          }, 
          {
            "familyName": "Timotin", 
            "givenName": "D.", 
            "type": "Person"
          }, 
          {
            "familyName": "Vasilescu", 
            "givenName": "F.-H.", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-0348-8575-1_7", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-3-0348-9687-0", 
            "978-3-0348-8575-1"
          ], 
          "name": "Operator Extensions, Interpolation of Functions and Related Topics", 
          "type": "Book"
        }, 
        "name": "Quasi-Contractions on Kre\u012dn Spaces", 
        "pagination": "123-148", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1040296755"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-0348-8575-1_7"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "bff4e048848667879e35428e67b2a6b67eab897bcf2a55b945c4ea3512517c1c"
            ]
          }
        ], 
        "publisher": {
          "location": "Basel", 
          "name": "Birkh\u00e4user Basel", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-0348-8575-1_7", 
          "https://app.dimensions.ai/details/publication/pub.1040296755"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-16T08:59", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000369_0000000369/records_68978_00000000.jsonl", 
        "type": "Chapter", 
        "url": "https://link.springer.com/10.1007%2F978-3-0348-8575-1_7"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8575-1_7'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8575-1_7'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8575-1_7'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8575-1_7'


     

    This table displays all metadata directly associated to this object as RDF triples.

    95 TRIPLES      23 PREDICATES      33 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-0348-8575-1_7 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N660e0eb2d0cc4dddace6882073fbfa69
    4 schema:citation sg:pub.10.1007/978-3-0348-7701-5_5
    5 sg:pub.10.1007/978-3-642-65567-8
    6 sg:pub.10.1007/bfb0069840
    7 https://doi.org/10.1002/mana.19770770116
    8 https://doi.org/10.1016/0022-1236(92)90124-2
    9 https://doi.org/10.1307/mmj/1029003552
    10 schema:datePublished 1993
    11 schema:datePublishedReg 1993-01-01
    12 schema:description A quasi-contraction, acting between Kreĭn spaces, is a linear bounded operator which is contractive when restricted to some subspace of finite codimension. If, in addition, the same property is satisfied by the adjoint of the operator, then it is called a double quasi-contraction. This paper is devoted to the investigation of basic properties of quasi-contractions and double quasi-contractions. Among others, we prove that the compression of a quasi-contraction (double quasi-contraction) to maximal uniformly negative subspaces is a semi-Fredholm operator (respectively, Fredholm operator) and we give a formula to compute its index. A spectral characterization of double quasi-contractions within the class of quasi-contractions is also obtained.
    13 schema:editor N9027860dd9334f1b895eb87053944608
    14 schema:genre chapter
    15 schema:inLanguage en
    16 schema:isAccessibleForFree false
    17 schema:isPartOf Nf70ad697602342db84863d8ae720f800
    18 schema:name Quasi-Contractions on Kreĭn Spaces
    19 schema:pagination 123-148
    20 schema:productId N429250cb88814fc0929a2483dab7da51
    21 Nd260b331798043fa9621c8ee88f5bd1e
    22 Nd286950373254209b017be2a3b5c7892
    23 schema:publisher N0f7b92fac526491e8e6bba6fe59b474f
    24 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040296755
    25 https://doi.org/10.1007/978-3-0348-8575-1_7
    26 schema:sdDatePublished 2019-04-16T08:59
    27 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    28 schema:sdPublisher N56ba320722d54192987a270f36e2b2ca
    29 schema:url https://link.springer.com/10.1007%2F978-3-0348-8575-1_7
    30 sgo:license sg:explorer/license/
    31 sgo:sdDataset chapters
    32 rdf:type schema:Chapter
    33 N0f7b92fac526491e8e6bba6fe59b474f schema:location Basel
    34 schema:name Birkhäuser Basel
    35 rdf:type schema:Organisation
    36 N3d0858e8e4f845858fbe8947661c5117 rdf:first N7bbbabf3c53c4faf9fcc90a3ba7ada8c
    37 rdf:rest rdf:nil
    38 N429250cb88814fc0929a2483dab7da51 schema:name readcube_id
    39 schema:value bff4e048848667879e35428e67b2a6b67eab897bcf2a55b945c4ea3512517c1c
    40 rdf:type schema:PropertyValue
    41 N56ba320722d54192987a270f36e2b2ca schema:name Springer Nature - SN SciGraph project
    42 rdf:type schema:Organization
    43 N660e0eb2d0cc4dddace6882073fbfa69 rdf:first sg:person.016700571527.26
    44 rdf:rest rdf:nil
    45 N7393399cc4ab474ca131e8606cd3bbd7 schema:familyName Timotin
    46 schema:givenName D.
    47 rdf:type schema:Person
    48 N7bbbabf3c53c4faf9fcc90a3ba7ada8c schema:familyName Vasilescu
    49 schema:givenName F.-H.
    50 rdf:type schema:Person
    51 N9027860dd9334f1b895eb87053944608 rdf:first Neca6e399ad0a4620a01211de79f13361
    52 rdf:rest Ne5a04689231940fcaeaabb06cbba70fc
    53 Nc04b0084b7744d4fb993811d9c2be4ef schema:name Institutul de Matematică, al Academiei Române, C.P. 1-764, 70700, Bucureşti, România
    54 rdf:type schema:Organization
    55 Nd260b331798043fa9621c8ee88f5bd1e schema:name doi
    56 schema:value 10.1007/978-3-0348-8575-1_7
    57 rdf:type schema:PropertyValue
    58 Nd286950373254209b017be2a3b5c7892 schema:name dimensions_id
    59 schema:value pub.1040296755
    60 rdf:type schema:PropertyValue
    61 Ne5a04689231940fcaeaabb06cbba70fc rdf:first N7393399cc4ab474ca131e8606cd3bbd7
    62 rdf:rest N3d0858e8e4f845858fbe8947661c5117
    63 Neca6e399ad0a4620a01211de79f13361 schema:familyName Gheondea
    64 schema:givenName A.
    65 rdf:type schema:Person
    66 Nf70ad697602342db84863d8ae720f800 schema:isbn 978-3-0348-8575-1
    67 978-3-0348-9687-0
    68 schema:name Operator Extensions, Interpolation of Functions and Related Topics
    69 rdf:type schema:Book
    70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    71 schema:name Mathematical Sciences
    72 rdf:type schema:DefinedTerm
    73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    74 schema:name Pure Mathematics
    75 rdf:type schema:DefinedTerm
    76 sg:person.016700571527.26 schema:affiliation Nc04b0084b7744d4fb993811d9c2be4ef
    77 schema:familyName Gheondea
    78 schema:givenName Aurelian
    79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016700571527.26
    80 rdf:type schema:Person
    81 sg:pub.10.1007/978-3-0348-7701-5_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026233832
    82 https://doi.org/10.1007/978-3-0348-7701-5_5
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/978-3-642-65567-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011407145
    85 https://doi.org/10.1007/978-3-642-65567-8
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/bfb0069840 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006857348
    88 https://doi.org/10.1007/bfb0069840
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.1002/mana.19770770116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027367955
    91 rdf:type schema:CreativeWork
    92 https://doi.org/10.1016/0022-1236(92)90124-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043655855
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1307/mmj/1029003552 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064976412
    95 rdf:type schema:CreativeWork
     




    Preview window. Press ESC to close (or click here)


    ...